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3.1CH3 Waves

General Properties of Waves — Cambridge O Level Physics 5054 Revision Notes & Topical Questions

10 min read 13 parts Lesson 1 of 4

📚 Cambridge O Level Physics 5054 Hub / Topical Revision
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Part 1 of 11What waves do

  • Wave
    • a disturbance that transfers energy from one place to another without transferring matter.
    • Particles of the medium oscillate about fixed positions but do not travel with the wave.
  • Wave source
    • an oscillation produces the wave, such as a vibrating hand, a loudspeaker cone or a ripple dipper.
  • Examples
    • water waves, sound waves, light, seismic waves and waves in a rope or spring.
  • Medium
    • mechanical waves need a medium to travel through, but electromagnetic waves can travel through a vacuum.
  • Demonstrating that matter does not travel
    • a cork on a water surface bobs up and down as the waves pass but does not move along.

Part 2 of 11Transverse and longitudinal waves

  • Transverse wave
    • the oscillations of the particles are at right angles to the direction of energy transfer.
    • Examples are water ripples, light and all electromagnetic waves, and waves on a rope.
  • Longitudinal wave
    • the oscillations are parallel to the direction of energy transfer, forming compressions and rarefactions.
    • Sound waves and seismic P waves are longitudinal.
  • Compression
    • a region where the particles are closer together and the pressure is higher.
  • Rarefaction
    • a region where the particles are further apart and the pressure is lower.
FeatureTransverseLongitudinal
Direction of oscillationPerpendicular to wave travelParallel to wave travel
PatternPeaks (crests) and troughsCompressions and rarefactions
ExamplesLight, water waves, ropeSound, slinky push-pull
Travel throughSolids, surfaces of liquids, vacuum (EM)Solids, liquids and gases
Polarisation possibleYesNo

Part 3 of 11Wave quantities

  • Amplitude (a)
    • the maximum displacement of a particle from its rest position, measured in metres.
    • A larger amplitude means a wave carrying more energy.
  • Wavelength (λ)
    • the distance between two consecutive points in phase, such as crest to crest, in metres.
  • Frequency (f)
    • the number of complete waves passing a point per second, in hertz (Hz).
      • (or oscillations)
  • Period (T)
    • the time for one complete wave or oscillation, T = 1 ÷ f.
      What the symbols mean: T = period, the time for one complete wave (s) · f = frequency (Hz)
    • A frequency of 50 Hz has a period of 0.020 s.
  • Wave speed (v)
    • the distance travelled by a wave crest per second, in m/s.
  • Wavefront
    • a line joining points that are in the same state of oscillation, such as the crests.
  • Reading a displacement-distance graph
    • the amplitude is the maximum height from the centre line, and the wavelength is the horizontal length of one cycle.
  • Reading a displacement-time graph
    • the horizontal length of one cycle gives the period, from which f = 1 ÷ T.

Part 4 of 11The wave equation

  • Equation
    • wave speed = frequency × wavelength, or v = fλ.
    • v in m/s, f in Hz and λ in m.
  • Why it works
    • in one period T the wave moves forward one wavelength, so v = λ ÷ T = fλ.
  • Constant speed
    • in a given medium the speed is fixed, so a higher frequency means a shorter wavelength.
    • This is why a short-wavelength high-pitched sound has a high frequency.
  • Effect of changing medium
    • when a wave enters another medium, its frequency stays the same, but the speed and wavelength change.
  • Using the equation
    • rearrange to f = v ÷ λ or λ = v ÷ f.
    • Convert prefixes such as MHz to Hz before calculating.

Part 5 of 11Waves in a ripple tank

  • Ripple tank
    • a shallow tank of water with a vibrating dipper or bar that produces waves, lit from above to show wavefronts on a screen below.
  • Using a stroboscope
    • a flashing light at the wave frequency makes the wave pattern appear to stand still, so wavelengths can be measured.
  • Measuring wave speed
    • measure the wavelength on the screen and the frequency of the dipper, then use v = fλ.
  1. Set the dipper vibrating at a known frequency.
  2. Freeze the pattern with a strobe light.
  3. Measure the distance across several wavefronts and divide by the number of waves to get λ.
  4. Calculate v = fλ.
  • Deeper and shallower water
    • waves travel faster in deeper water and slower in shallow water.
    • The wavelength is longer in deep water for the same frequency.

Part 6 of 11Reflection of waves

  • Reflection
    • a wave bounces back when it hits a barrier.
  • Law of reflection
    • the angle of incidence equals the angle of reflection.
    • Both angles are measured from the normal, the line at right angles to the surface.
  • Wavefront view
    • straight wavefronts reflect from a straight barrier with the same wavelength, speed and frequency.
  • Curved reflectors
    • a concave reflector focuses plane waves to a point, as in satellite dishes.
  • Echoes
    • sound reflected from a hard surface returns as an echo, used in sonar and in measuring depth.

Part 7 of 11Refraction of waves

  • Refraction
    • the change in direction of a wave when it passes from one medium to another because its speed changes.
  • Frequency and speed
    • the frequency stays the same, the wavelength changes with speed, so a slower wave has a shorter wavelength.
  • Direction of bending
    • moving into a slower region bends the wave toward the normal, and moving into a faster region bends it away.
    • In a ripple tank, a glass plate makes shallow water, so wavefronts bunch up and bend toward the normal.
  • Along the normal
    • a wave travelling along the normal changes speed and wavelength but does not change direction.
  • Examples
    • light refracting in glass, sound curving over cold air at night, and water waves bending near a shore.

Part 8 of 11Diffraction

  • Diffraction
    • the spreading out of a wave as it passes through a gap or around an obstacle.
  • Effect of gap size
    • the effect is greatest when the gap is about the same size as the wavelength.
    • A narrow gap produces circular waves, and a wide gap lets the waves through with only slight bending at the edges.
  • Wavelength and diffraction
    • longer wavelengths diffract more, so long radio waves bend around hills and low sounds go around corners.
  • Unchanged properties
    • the frequency, speed and wavelength do not change during diffraction.
  • Everyday evidence
    • you hear a person around a corner before you see them because sound waves have a much longer wavelength than light and diffract more.

Part 9 of 11Wave features and examples in ropes, springs and seismic waves

  • Crest and trough
    • a crest (peak) is a point of maximum upward displacement and a trough is a point of maximum downward displacement.
  • Waves in ropes and springs
    • flicking a rope up and down gives a transverse pulse, and pushing and pulling a slinky gives compressions and rarefactions.
  • Frequency definition
    • the number of wavelengths that pass a point each second, measured in hertz.
  • Seismic waves
    • earthquakes send out two kinds of wave through the Earth.
Seismic waveTypeDirection of vibrationTravel
P-wave (primary)LongitudinalParallel to the energy transferFaster, through solids and liquids
S-wave (secondary)TransverseAt right angles to the energy transferSlower, through solids only
  • Light and water waves
    • electromagnetic waves and waves on water surfaces are also transverse.

Part 10 of 11Ripple tank demonstrations

  • Reflection
    • straight waves meet a flat barrier, and the reflected wavefronts leave at the same angle to the barrier as they arrive.
  • Refraction
    • a submerged glass plate makes the water shallow, so the waves slow down and the wavelength shortens.
    • Waves that meet the boundary at an angle also change direction.
  • Diffraction through a gap
    • straight waves pass through a gap in two barriers and spread out.
    • A gap about the size of the wavelength gives almost circular waves, and a gap much wider than the wavelength gives little spreading.
  • Diffraction at an edge
    • waves bend round the end of a single barrier into the region behind it.
    • Waves of longer wavelength bend round the edge more than waves of shorter wavelength.
  • Changing the wavelength
    • slowing the dipper lowers the frequency and increases the wavelength, so the diffraction effect becomes stronger.

Part 11 of 11Worked examples

  1. A water wave has a frequency of 5.0 Hz and a wavelength of 0.12 m. Find its speed. [2]2 marks

  2. A radio station transmits at 96 MHz. The speed of radio waves is 3.0 × 108 m/s. Find the wavelength. [3]3 marks

  3. A displacement-time graph shows one complete wave taking 0.040 s. Find the frequency, and the wavelength if the wave speed is 340 m/s. [3]3 marks

  4. Waves of wavelength 2.0 cm and speed 8.0 cm/s pass into shallower water where the speed is 4.0 cm/s. State the new frequency and wavelength. [3]3 marks

  5. Describe what happens to waves as they pass through a gap that is much smaller than their wavelength. [2]2 marks

  6. A ripple tank wave has frequency 8.0 Hz and wavelength 0.020 m. The wave enters shallow water and the wavelength becomes 0.012 m. Find the new speed. [3]3 marks

Key terms

TermMeaning
WaveA disturbance that transfers energy without transferring matter.
WavelengthThe distance between two consecutive points in phase on a wave.
FrequencyThe number of complete waves or oscillations per second, in hertz.
AmplitudeThe maximum displacement from the rest position.
RefractionA change in wave direction caused by a change in speed at a boundary.
DiffractionThe spreading of waves through a gap or around an obstacle.
WavefrontA line joining points in the same phase of a wave.
CompressionA region of higher pressure in a longitudinal wave.

Avoid these mistakes

  1. Thinking the particles travel with the wave — they oscillate about a fixed position while the energy moves.
  2. Mixing up the amplitude with the peak-to-peak height — amplitude is from the rest position to the crest.
  3. Saying frequency changes at refraction — frequency is set by the source and stays constant.
  4. Measuring angles from the surface — angles of incidence and reflection are measured from the normal.
  5. Using MHz or cm directly in v = fλ — convert to Hz and metres first.

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